UBC Theses and Dissertations
Optimal design for linear regression with variable costs and precision requirements and its applications to forestry Penner, Margaret
Various criteria are discussed and as algorithms for obtaining optimal designs for use in linear regression. Linear regression is used widely and effectively in forestry but the method of quantifying the linear relationship in terms of selecting observations or designing an experiment to obtain observations is often inefficient. The experiment or study objectives must be identified to develop a criterion for comparing designs. Then a method of obtaining observations can be found which performs well under this criterion. Biometricians in forestry have been slow to take advantage of one of the assumptions of linear regression, namely that the independent variables are fixed. In part this has been due to limitations in the theory. Two important assumptions in most optimal design work, namely that precision requirements and costs are constant for all observations, are not valid for most forestry applications. Ignoring nonconstant costs can lead to designs less efficient than ones where each combination of independent variables is selected with the same frequency. The objective of this study was to develop a method of optimal sample selection that allowed for costs and precision requirements that vary from observation to observation. The resulting practical experimental layouts are more efficient for attaining the experimenter's objectives than randomly selected observations or designs constructed using the currently available design theory. Additional features of designs that consider differing costs and precision requirements are their larger sample size and their robustness to misspecification of the sample space. Traditional optimal designs concentrated observations on the boundaries of the sample space. By recognizing that these observations may be more costly and may not be of primary interest to the experimenter, more efficient designs can be constructed from less extreme observations. A computer program for obtaining optimal designs is also included.
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